Quantitative Aptitude Quiz! Trivia

Explanation
The product of two numbers is given as 16200. The LCM (Least Common Multiple) of the two numbers is given as 216. To find their HCF (Highest Common Factor), we can use the relationship between HCF and LCM. The product of two numbers is equal to the product of their HCF and LCM. Therefore, we can divide the product of the two numbers by their LCM to find their HCF. In this case, 16200 divided by 216 equals 75, which is the HCF of the two numbers.

Explanation
The population of the village decreases at a rate of 20% per annum. This means that every year, the population decreases by 20% of its current value. So, after 2 years, the population would have decreased by 40% (20% x 2) from its initial value of 10,000. To find the present population, we subtract 40% of 10,000 from 10,000, which gives us 6,000. Therefore, the correct answer is 6,400.

Explanation
If Ravi receives 84 toffees, and the ratio of distribution is 2:3:7, we can find the total number of toffees distributed by dividing 84 by the ratio of Ravi's share, which is 3. This gives us 28 toffees per unit of the ratio. To find the total, we multiply 28 by the sum of the ratio's units, which is 2+3+7=12. Therefore, the total number of toffees distributed is 28*12=336.

Explanation
The remaining number must be 50. This can be determined by finding the sum of the first three numbers (40 x 3 = 120) and the sum of the last three numbers (60 x 3 = 180). The sum of all seven numbers would be 120 + 180 = 300. Since the average of all seven numbers is 50, the sum of all seven numbers must be 50 x 7 = 350. Therefore, the remaining number must be 350 - 300 = 50.

Explanation
When a discount of 15% is applied to the list price of Rs. 300, the selling price becomes 85% of Rs. 300, which is Rs. 255. Then, when a discount of 10% is applied to the selling price of Rs. 255, the final selling price becomes 90% of Rs. 255, which is Rs. 229.5. Therefore, the correct answer is 229.5.

Explanation
When the price of a pair of shoes is decreased by 10%, it means that the price is reduced by 10%. As a result of this price reduction, the number of pairs sold increases by 20%. This increase in the number of pairs sold compensates for the decrease in price, resulting in an overall net effect of an 8% increase in sales.

Explanation
Since B and C can do the work in 15 and 20 days respectively, their combined work rate is 1/15 + 1/20 = 7/60. After working for 5 days, they have completed 5*(7/60) = 7/12 of the work. Therefore, the remaining work is 1 - 7/12 = 5/12. Since A can finish the project in 30 days, his work rate is 1/30. Therefore, it will take A 30*(5/12) = 12.5 days to complete the remaining work.

Explanation
The difference in speed between the two scenarios is 60 kmph - 50 kmph = 10 kmph. This means that for every hour of travel, the train is delayed by 10 km. Since the train is 15 minutes late when traveling at 50 kmph, which is 1/4 of an hour, the total delay is 1/4 * 10 km = 2.5 km. Therefore, the length of the journey is the distance covered by the train at 60 kmph, which is the on-time scenario, minus the delay of 2.5 km. So, the length of the journey is 60 km - 2.5 km = 57.5 km.

Explanation
To find the number of ways the letters of the word 'lemon' can be formed such that the vowels do not come together, we can use the principle of permutation. The word 'lemon' has 5 letters, with 2 vowels (e and o) and 3 consonants (l, m, and n).

First, let's consider the vowels as a single entity. We can arrange this entity and the consonants in 4! = 24 ways.

However, within the vowels entity, the vowels 'e' and 'o' can be arranged in 2! = 2 ways.

Therefore, the total number of ways to arrange the letters of 'lemon' such that the vowels do not come together is 24 * 2 = 48.

However, this only accounts for one possible arrangement of the vowels. To find all possible arrangements, we multiply by the number of ways the vowels can be arranged, which is 2!.

Hence, the correct answer is 48 * 2 = 72.

Explanation
The probability of Suresh answering each question correctly is 1/2 since there are only 2 answer options for each question. Since the questions are independent of each other, the probability of answering all 20 questions correctly is obtained by multiplying the individual probabilities together. Therefore, the probability is (1/2)^20.

Explanation
If 10 boys can eat 10 chocolates in 10 minutes, it means that each boy can eat one chocolate in 10 minutes. Therefore, 1 boy can eat 1 chocolate in 10 minutes.

Explanation
When the price of sugar increases by 20%, the expenditure on sugar also increases by the same percentage. In order to maintain the same expenditure, the decrease in consumption should be equivalent to the increase in price. To find the percentage decrease, we can use the formula (increase/decrease percentage = (100 x increase/decrease amount)/original amount). Plugging in the values, we get (20/120) x 100 = 16.66%. Therefore, the percentage decrease in the consumption of sugar to maintain the same expenditure is 16.66%.

Explanation
To find the highest power of 5 in 30!, we need to count the number of times 5 appears as a factor in the prime factorization of 30!. Since 5 is a prime number, it only appears once as a factor in each multiple of 5. Therefore, we need to count the number of multiples of 5 from 1 to 30. There are 6 multiples of 5 (5, 10, 15, 20, 25, and 30) in the range of 1 to 30. However, 25 and 30 have an additional factor of 5, so we count them twice. Therefore, the highest power of 5 in 30! is 5^6 * 5^1 = 5^7.

Explanation
The man rows a boat at a speed of 15 km/hr. It takes him 4 hours and 30 minutes to row a boat to a place 30 km away and return. To find the speed of the river, we can use the formula: Speed of boat in still water = (Speed downstream + Speed upstream) / 2. Let's assume the speed of the river is x km/hr. The speed downstream would be (15 + x) km/hr, and the speed upstream would be (15 - x) km/hr. Since the distance is the same for both directions, we can set up the equation: 30 = [(15 + x) + (15 - x)] / 2 * 4.5. Simplifying this equation, we get 30 = (30 * 4.5) / 2, which gives us x = 5 km/hr. Therefore, the speed of the river is 5 km/hr.

Explanation
The total number of factors in a number can be found by prime factorizing the number and then adding 1 to each exponent in the prime factorization, and finally multiplying all these numbers together. The prime factorization of 400 is 2^4 * 5^2. Adding 1 to each exponent gives us (4+1) * (2+1) = 5 * 3 = 15. Therefore, the total number of factors in 400 is 15.